Please I need help to fix this gauss seidel code, I feel like its not well-written because 1- if I increase the number of nodes, it gives the output as "NaN" 2-it doesn't converge..

I'm trying to solve the energy balance equation of some component of a flat plate solar collector( glass cover, air gap, absorber and HTF) using gauss seidel. I have written the below code but something is wrong with it because 1- if I increase the number of nodes, it gives output the as "NaN" unless I reduce the time step 2-it doesn't converge.

    function [T_siedal,x,iter,error] = Gauss_S(Nx,Ny,aE,aW,aN,aS,aNN,aSS,b,aP,delx,T_am)
    %N_x no of nodes in the x-direction
    %N_y no of nodes in the y-direction
    % x - x-position (m)
    % y - y-position (m)

    %Setup grid

    for i=1:Nx
    x(i,1)=(i-1)*delx;
    end
    maxiter=10000;
    T_guess=zeros(Nx,Ny);
    T=T_guess;
    tol=0.00000001;
    error=1;
    iter = 0;
    %%boundary condition at inlet of HTF
    for i=1:Nx
         for j=1:Ny
       if  i==1 && j==1   
       T(i,j)=T_am;
       end
         end
     end

    while (error>tol && iter<maxiter)
        T_old=T;
        for i=1:Nx  
               if i==1             
           %%HTF equation

           %%Absorber Equation      
                  j=2;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aN(i,j+1)*T(i,j+1))+(aS(i,j-1)*T(i,j-1))+(aNN(i,j+2)*T(i,j+2))+(b(i,j)))/aP(i,j);   

       %%Air Gap Equation
                  j=3;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aN(i,j+1)*T(i,j+1))+(aS(i,j-1)*T(i,j-1))+(b(i,j)))/aP(i,j);

       %%Glass Cover Equation     
                  j=4;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aS(i,j-1)*T(i,j-1))+(aSS(i,j-2)*T(i,j-2))+(b(i,j)))/aP(i,j);     
               elseif i>1 && i<Nx             
           %%HTF equation      
                  j=1;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aW(i-1,j)*T(i-1,j))+(aN(i,j+1)*T(i,j+1))+(b(i,j)))/aP(i,j);

       %%Absorber Equation   
                  j=2;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aW(i-1,j)*T(i-1,j))+(aN(i,j+1)*T(i,j+1))+(aS(i,j-1)*T(i,j-1))+(aNN(i,j+2)*T(i,j+2))+(b(i,j)))/aP(i,j); 

           %%Air Gap Equation     
                  j=3;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aW(i-1,j)*T(i-1,j))+(aN(i,j+1)*T(i,j+1))+(aS(i,j-1)*T(i,j-1))+(b(i,j)))/aP(i,j); 

           %%Glass Cover Equation  
                  j=4;
       T(i,j)=((aE(i+1,j)*T(i+1,j))+(aW(i-1,j)*T(i-1,j))+(aS(i,j-1)*T(i,j-1))+(aSS(i,j-2)*T(i,j-2))+(b(i,j)))/aP(i,j);  

               else              
            %%HTF equation      
                  j=1;
       T(i,j)=((aW(i-1,j)*T(i-1,j))+(aN(i,j+1)*T(i,j+1))+(b(i,j)))/aP(i,j);

            %%Absorber Equation   
                  j=2;
       T(i,j)=((aW(i-1,j)*T(i-1,j))+(aN(i,j+1)*T(i,j+1))+(aS(i,j-1)*T(i,j-1))+(aNN(i,j+2)*T(i,j+2))+(b(i,j)))/aP(i,j); 

            %%Air Gap Equation

                  j=3;
       T(i,j)=((aW(i-1,j)*T(i-1,j))+(aN(i,j+1)*T(i,j+1))+(aS(i,j-1)*T(i,j-1))+(b(i,j)))/aP(i,j);  

            %%Glass Cover Equation      
                  j=4;
       T(i,j)=((aW(i-1,j)*T(i-1,j))+(aS(i,j-1)*T(i,j-1))+(aSS(i,j-2)*T(i,j-2))+(b(i,j)))/aP(i,j);     
               end
        end
        error = norm(T-T_old)/norm(T);
        iter = iter+1;
    end

    T_siedal=T

    end

          if true
        % code
      end

[John D'Errico]

Oh, sure. Does not converge, and results in NaN. So what is wrong with that? Some people are soooo picky. I'm sure your instructor won't notice a minor flaw like that.

Seriously, I might create the full matrix, to verify that the matrix is non-singular.

Next, Gauss-Seidel is not always convergent. The classic requirement that I recall is diagonal dominance. Without that, don't expect convergence. That might also explain the NaNs.

Finally I'd suggest a careful check of the equations you wrote. But without spending a fair amount of time to dig into what you have written, that is something that you are the best person to check.

If this is not homework, then why in the name of god and little green apples are you using Gauss-Seidel to solve a linear system of equations?

Instead, you should learn to use sparse matrices. Formulate the problem as a sparse matrix. Then use backslash to solve the system. Create the sparse matrix in ONE step using sparse, from a list of row and column indices and elements of the matrix. This is by FAR preferable to use of Gauss-Seidel. If it is indeed homework, then do as you are required. Teachers can be picky.

[Gadosky571]

thanks for the suggestion John. I'm new to Matlab that's why but I will see if I can solve it using backslash. its part of my project not a homework. Thanks once again.

[Rohit Bhise]

Hey I'm also having the same problem. I'm trying to solve cavity problem with symmetric coupled Gauss sidel method and I'm getting NAN values. Did you find solution to your problem?